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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

6. Recursively Defined Sequences

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Exercise 45 Page 319

The recursive equation for an arithmetic sequence is of the form a_n=a_(n-1)+d.

Error: The common difference is - 12, not 12.
Explicit Rule: a_n=18-12n

Practice makes perfect

Recall that the recursive equation for an arithmetic sequence is of the following form. a_n=a_(n-1)+ d Here d is the common difference. Then, for the given sequence, the common difference is - 12. a_n=a_(n-1)-12 ⇔ a_n=a_(n-1)+ ( - 12) The explicit formula for the sequence, with first term a_1=6 and common difference - 12, can be written as follows. a_n=a_1+(n-1)d ⇒ a_n= 6+(n-1)( - 12) Let's simplify it.

a_n=6+(n-1)(- 12)

Distribute (- 12)

a_n=6-12n+12

Add terms

a_n=18-12n

The explicit rule for the sequence is a_n=18-12n. Correct: & a_n=18-12n ✓ Incorrect: & a_n=- 6+12n *

Subchapter links

Communicate Your Answer p.313

Monitoring Progress p.315-317

Exercises p.318-320